IET Microwaves, Antennas & Propagation Research Article
Compensation method for distorted planar array antennas based on structural– electromagnetic coupling and fast Fourier transform
ISSN 1751-8725 Received on 5th September 2017 Revised 27th November 2017 Accepted on 7th December 2017 E-First on 15th February 2018 doi: 10.1049/iet-map.2017.0814 www.ietdl.org
Congsi Wang1,2, Yan Wang1 , Jinzhu Zhou1, Meng Wang3, Jianfeng Zhong4, Baoyan Duan1 1Key
Laboratory of Electronic Equipment Structure Design, Ministry of Education, Xidian University, Xi'an 710071, People's Republic of China of Civil and Environmental Engineering, University of New South Wales, Sydney 2052, Australia 3Research Institute of Shaanxi Huanghe Group Co., Ltd, Xi'an 710043, People's Republic of China 4Nanjing Research Institute of Electronics Technology, Nanjing 210039, People's Republic of China E-mail:
[email protected] 2School
Abstract: Complex operating environment could introduce serious degradation to the electromagnetic performance of active phased array antenna in both the main lobe and sidelobe areas. The effective compensation techniques become the key for antenna to perform in reliable service condition. Therefore, a method combined coupled structural-electromagnetic model with two-dimensional fast Fourier transform for compensation is presented. A compensation calculation model of the excitation current for planar array is established accordingly, quantitatively expressing the relationship between the excitation current compensation and the structure error. The adjustment quantities of excitation amplitude and phase can be quickly obtained and implemented to recover a high-quality pattern from a distorted antenna in both the main lobe and sidelobe areas. Lastly, the simulation of the space-based array antenna is illustrated to compensate its property under the impact of space environment and heat power from its electric devices. Furthermore, an experiment platform of an X-band active phased array antenna with 32 × 24 elements is built and tested for the electromagnetic performance compensation. The simulation and experimental results show that the proposed method can guarantee the performance of the service antenna quickly and effectively in the whole observation area.
1 Introduction High in reliability, multi in function, strong in tracking and detecting, active phased array antennas are widely applied in radar systems [1–3]. With rapid development of military technology, radars are required for better target identification, stronger antijamming ability, and more reliable stability, which lead to high demand for the performance of antenna. However, complex operating environment causes structural deformation and introduces serious degradation to the property of antennas [4–6]. For example, the space-based array antennas are subjected to long term of sunshine and low-temperature heat sink in space when working at near earth orbit. Also at the time of entering and leaving the earth shallow, high-temperature gradient could be caused [7]. As a result, thermal deformation is caused and directly leads to the degradation or even failure of the antenna's performance. Therefore, it is an urgent need to take advantage of compensation techniques to guarantee the service performance for active phased array antennas. Commonly, there are two compensation techniques used to guarantee the service performance of array antennas, which are the structural and electronic compensation methods, respectively. By adjusting the mechanical devices such as the actuators, structure errors are reduced and following the precision of antenna array is improved when employing the structure compensation. However, large amount of adjustment mechanisms increase the weight and complexity of antenna system. In addition, real-time compensation cannot be achieved in this way. Electronic compensation puts use of changing the excitation current to realise the performance compensation. Its effectiveness mainly depends on the accurate adjustment amount of current. At present, some scholars have focused on adjusting the excitation phase to compensate the performance of array antennas. Son et al. [8] changed the phase by adjusting the length of cable of the phased shifter to eliminate the pointing error for a stair-planar IET Microw. Antennas Propag., 2018, Vol. 12 Iss. 6, pp. 954-962 © The Institution of Engineering and Technology 2017
phased array. Knott [9] applied the phase compensation for conformal array antenna and found that the compensation is valid for the effect of low-order vibration modes in reducing the pointing error. In addition, an optimisation of the phase with genetic algorithm to achieve the goal of maximising the gain of the phased array antenna was also discussed [10]. Takano et al. [11] put forward the phase compensation to reduce the phase deterioration and adjusted the direction of the main beam to be the target value for a multiple folding phased array. In conclusion, the phase compensation is mainly applied for the compensation of gain and pointing error. It is effective in the main lobe area but not evident in the sidelobe area for array antennas. To overcome this problem, the adjustment of both the excitation amplitude and phase is presented. Lesueur et al. [12] used the least square method and spectral analysis to give the compensation amounts of amplitude and phase. However, only the linear array antenna with transverse displacement was considered. Arnold et al. [13] proposed that for real array antenna, both the amplitude and phase changed occur during the deformation process, so the excitation current should be adjusted not only the phase but also the amplitude. However, there is lack of figuring out the adjustment amounts of the amplitude and phase corresponding to the deformation for planar array antenna. Therefore, a compensation method based on the structure– electromagnetic coupling model and two-dimensional fast Fourier transform is presented to quantitatively give the relationship between the compensation amounts of excitation amplitude and phase and the structure error for planar array antenna. The compensation method is implemented to recover a high-quality pattern from a distorted antenna in both the main lobe and sidelobe areas.
954
position errors for the ground-based antenna as well as the spacebased antenna on orbit. Suppose the position error of the m, n th 0 ≤ m ≤ M − 1, 0 ≤ n ≤ N − 1 element is Δxmn, Δymn, Δzmn . Based on the coupled structuralelectromagnetic model, the property of the deformed planar array antenna [21] is E u, v =
M−1N−1
∑ ∑ Imnexp
jk mdx + Δxmn − Δx0, 0 u + (ndy
m=0n=0
2
(1)
2
+Δymn − Δy0, 0 v+ Δzmn − Δz0, 0 1 − u − v Fig. 1 Diagram of planar active phased array antenna
2 Compensation calculation model of excitation current for planar array antenna Suppose that the elements of a planar active phased array antenna are arranged in rectangular grid as shown in Fig. 1, and there exist M × N array elements, which are arranged in xoy plane with intervals dx and dy, respectively. Complex service environment could cause the array antenna to produce the structure distortion, which could lead to the position deviation of element. In order to obtain the element position error, non-contact measurement and contact measurement are employed at present. The total station system measurement and digital photogrammetry etc. are the main application methods for non-contact measurement. With regard to the total station system measurement, the application of micro-triangulation with DAEDALUS system in total station is conceivable at an accuracy level of 10 μm for object with the size in the order of 1–3 m [14]. For digital photogrammetry, the digital close-range photogrammetry can be employed in a satellite antenna with the approximate diameter of 500 mm and the maximum value of RMS is tested as 0.048 mm for repetitive measurement accuracy [15]. The requirements of noncontact measurement are the stable measurement benchmark and enough space without sheltering. The contact measurement utilises the sensors to obtain the deformation of antenna. Sensors such as the passive optical probes [16] and WiSense unites [17] are commonly used in the measurement system. The optical probes are able to measure the displacement of an antenna with a resolution done to λ/1000 [16]. Data provided by the sensors combined with the original mechanical model allow the global shape of the distorted antenna structure and finally, the element position errors are achieved. In summary, the total station system measurement is suitable for the ground-based antenna. The passive optical probes could be applied in ground testing for a full reconstruction of the surface topography of array antenna. The WiSense unites have been employed in an antenna distortion measurement system to monitor the in-flight antenna distortion for a space-based synthetic aperture radar system in [17]. In addition, there are some more works applied in the deformation measurement for the space-based antenna on orbit. Haugse et al. [18] obtained the deformed shapes of a large space-based phased array antenna at various locations by employing the strain gauges as the deformation sensing devices combined with the strain-to-displacement algorithm. Li [19] acquired the deformations of a large planar phased array antenna by detecting the coherent radar returns for the space-based synthetic aperture radar. The method could be performed anywhere on orbit with no additional sensor and the deformations of small fractions (≤0.02) of a wavelength could be obtained. Besides, the Air Force Research Laboratory (AFRL) and the Jet Propulsion Laboratory (JPL) had presented a metrology system concept that a set of cameras were mounted in packs, in two positions above the centre plane of the array to continuously measure the element positions for a 50 m × 2 m space-based phased array in L-band. The system had been developed to meet the requirements without posing an unreasonable burden on mission resources in terms of cost, mass, power, and complexity in [20]. Therefore, the presented measurement methods above can measure and obtain the element
IET Microw. Antennas Propag., 2018, Vol. 12 Iss. 6, pp. 954-962 © The Institution of Engineering and Technology 2017
where Imn = Amnexp jφmn is the ideal excitation current, of which the magnitude part Amn and argument part φmn are the excitation amplitude and phase, respectively. u = sin θcos ϕ and v = sin θsin ϕ are the direction cosines with the direction of target relative to the x and y axes, respectively. k = 2π/λ is the wave constant. With small scale of structural error, (1) is expanded in the firstorder of Taylor series and approximately to be E u, v ≃
M−1N−1
∑ ∑ Imn
m=0n=0
1 + jk Δxmn − Δx0, 0 u
+ Δymn − Δy0, 0 v + Δzmn − Δz0, 0
(2)
× 1 − u2 − v2 exp jk mdxu + ndyv The ideal excitation current and the currents with structural errors in the x, y, and z directions are applied to the two-dimensional fast Fourier transform, respectively. Suppose that the plural αpq is the two-dimensional Fourier transform series of the ideal excitation current, then the ideal excitation current can be written as Imn =
1 MN
M−1N−1
∑ ∑ αpq ⋅ exp j2π
p=0 q=0
mp nq + M N
(3)
In the same way, suppose that the plurals βpq, γ pq and ζ pq are the two-dimensional Fourier transform series of the currents with position errors in x, y, and z directions, which are the items kImn Δxmn − Δx0, 0 , kImn Δymn − Δy0, 0 , and kImn Δzmn − Δz0, 0 , respectively. Finally, the property of the deformed planar array antenna can be written as E u, v =
1 MN
M−1N−1
∑ ∑
p=0 q=0
αpq + j βpqu + γ pqv + ζ pq
× 1 − u2 − v2 ⋅ × u+
M−1N−1
∑ ∑ exp
m=0n=0
jk mdx
(4)
pλ qλ + ndy v + Mdx Ndy
For the direction cosines u and v are continuous, they are replaced by up = − pλ/Mdx and vq = − qλ/Ndy, respectively. Then (4) can be written as E u, v ≃
M−1N−1
1 MN m=0n=0
∑ ∑
M−1N−1
∑ ∑
p=0 q=0
αpq + j βpqup + γ pqvq
+ζ pq 1 − u2p − vq2 ⋅ exp j2π
mp nq + M N
(5)
× exp jk mdxu + ndyv Two-dimensional fast Fourier inversion transform is then performed on the element excitation current in (5), that is
955
Fig. 2 Comparison of actual deformation and Taylor expansion in ϕ = 0∘ and ϕ = 90∘ planes
(a) In ϕ = 0∘ plane, (b) In ϕ = 90∘ plane
Fig. 3 Variation of gain and maximum sidelobe with normal position error
(6)
where ΔAmn and Δφmn are the adjustment quantities of amplitude and phase for deformed planar array antenna.
s is the equivalent excitation current of the deformed where Imn planar array antenna, which can be expressed as below
3 Discussion of maximum position error to be compensated
E u, v =
s Imn
1 = MN
M−1N−1
s ⋅ exp jk mdxu + ndyv ∑ ∑ Imn
m=0n=0
M−1N−1 M−1N−1
∑ ∑ ∑ ∑ Imn 1 + jk Δxmn − Δx
p=0 q=0
0, 0
m=0n=0
+ jk Δymn − Δy0, 0 vq + jk Δzmn − Δz0, 0 × 1 − u2p − vq2 exp − j2π × exp j2π
mp nq + M N
up (7)
mp nq + M N
Compared with the ideal excitation current, the compensation quantities of amplitude and phase for distorted array antenna are obtained s ΔAmn = Abs Imn /Abs Imn s Δφmn = Angle Imn − Angle Imn
956
(8)
An X-band active phased array antenna with elements of 32 × 32, and the intervals marked as dx = 0.5λ and dy = 0.5λ, respectively, are illustrated to discuss the maximum position error that can be compensated. Comparison of actual deformation and Taylor expansion in ϕ = 0∘ and ϕ = 90∘ planes is presented, as shown in Fig. 2. Systematic deformation is assumed as the distorted type for array antenna. The bowl shape deformation is selected as the systematic deformation type. A series normal errors with the maximum values from λ/10 to λ/3 are used for the comparison of actual deformation and Taylor expansion in planes ϕ = 0∘ and ϕ = 90∘, respectively. The variation of gain and maximum sidelobe with the normal position error is shown in Fig. 3, and the relationship between electromagnetic performance and normal error is listed in Table 1. An analysis of Fig. 3 and Table 1 reveals that the absolute relative changes of gain and maximum sidelobe levels in ϕ = 0∘ and ϕ = 90∘ planes increase with the increasing in normal position error. When the position error is λ/5, the relative changes of gain and maximum sidelobe levels in ϕ = 0∘ and ϕ = 90∘ planes are IET Microw. Antennas Propag., 2018, Vol. 12 Iss. 6, pp. 954-962 © The Institution of Engineering and Technology 2017
Table 1 Variation of electrical property with normal error Δzmn Relative change of gain, % Relative change of maximum sidelobe in ϕ = 0∘ plane, % λ/3 λ/4 λ/5 λ/6 λ/7 λ/8 λ/9 λ/10
11.14 7.05 4.86 3.54 2.69 2.11 1.69 1.39
14.32 9.02 6.21 4.52 3.43 2.69 2.16 1.77
Relative change of maximum sidelobe in ϕ = 90∘ plane, % −18.41 −15.86 −4.86 −3.62 −2.87 −2.31 −1.90 −1.58
Fig. 4 Model of space borne active phased array antenna (a) Antenna array, (b) Antenna feed layer
4.86, 6.21, and −4.86%, respectively. Once the error increases to λ/4, the relative change of maximum sidelobe level in ϕ = 90∘ plane changes greatly from −4.86 to −15.86%. In consideration of the relative changes of gain and maximum sidelobe as well as their variation trend, the position error λ/5 is selected to be the maximum error that the compensation method will be applied.
4 Simulation analysis As shown in Fig. 4, a space-based active phased array antenna is embedded with 32 × 16 elements, and the intervals are marked as dx = 0.85λ and dy = 0.75λ, respectively. The operating frequency is 9.375 GHz, and the initial excitation current for element is distributed equal in amplitude and phase. The compensation calculation model of the excitation current is used to compensate the thermal deformation under the effect of heat soak and thermal power consumption of electric devices in the feed layer of antenna system.
IET Microw. Antennas Propag., 2018, Vol. 12 Iss. 6, pp. 954-962 © The Institution of Engineering and Technology 2017
4.1 Electromagnetic performance analysis for heat soak and device thermal power The space-based phased array antenna is exposed to solar radiation when working at near earth orbit. Thus, selecting the extreme working condition of high temperature up to be 120°C. In addition, the power consumption of high-density devices, including the transmitter and receiver components, secondary electric power supplies, and wave control units, also causes the thermal deformation. The corresponding thermal power consumptions are 12, 20, and 15 W, respectively. Based on the finite method, firstly, the temperature field of antenna can be obtained, as shown in Fig. 5a. Applied with the sequential coupling, the temperatures of the nodes are served as the loads of structure and finally, the thermal deformation is given in Fig. 5b. As shown in Fig. 5a, the maximum temperature of the antenna is 168.26°C, which is mainly concentrated in the central of the antenna structure, and leads to the maximum thermal deformation of 5.77 mm, which is about λ/5 as in Fig. 5b. Using the coupled structural-electromagnetic model, the property of the deformed array antenna is shown in Fig. 6.
957
Fig. 5 Temperature distribution and thermal deformation (a) Temperature distribution, (b) Thermal deformation
Fig. 6 Comparison of property before and after deformation (a) In ϕ = 0∘ plane, (b) In ϕ = 90∘ plane
As shown in Fig. 6, the gain loss of the antenna is up to be 0.64 dB, and the maximum sidelobe level in ϕ = 0∘ plane is raised by 2.36 dB. Meanwhile, the main beam pointing errors of the two planes are both 0.08∘. It can be seen that the structure distortion greatly influences the gain and maximum sidelobe level. Moreover, the main beam direction is affected, too. To ensure the performance of the antenna, it is necessary to compensate the gain and sidelobe level. The beam pointing error needs to be compensated at the same time. Comparing the performances of the deformed array antenna in ϕ = 0∘ and ϕ = 90∘ planes as shown in Fig. 6, the performance of antenna in ϕ = 0∘ plane degrades more seriously. Thus, it is selected to use for the discussion of the compensation effect. 4.2 Compensation of electromagnetic performance of array antenna with thermal deformation To improve the performance of the space-based active phased array antenna due to thermal deformation, the amplitude and phase adjustments are calculated based on the proposed compensation calculation model of excitation current. The results are shown in Figs. 7a and b, from which we learn that the highest amplitude adjustment is 4.42 dB and the largest phase adjustment is 53.86°. Compared with the thermal deformation, the area of the maximum deformation is approximate corresponding to the most obvious area of the adjustment of excitation current, including both amplitude and phase distribution. Commonly, the phase-only compensation can also be applied for active phased array antenna. Therefore, the compensation with the phase-only adjustment is conducted and compared with the 958
proposed method. According to (1), the element position error leads to the spatial phase distribution error which is changing with the different azimuth and elevation angle. The phase-only compensation needs the fixing adjustment of phase corresponding to the spatial phase distribution error in a certain direction, which is usually selected as the main beam direction, for it is directly influencing the gain and pointing accuracy. The adjustment amount of the phase for planar array antenna is deduced as below Δφp = − jk Δxmn − Δx0, 0 us + Δymn − Δy0, 0 v s + Δzmn − Δz0, 0 1 − us2 − vs2
(9)
where us = sin θscos ϕs and vs = sin θssin ϕs, θs, ϕs represents the main beam direction. For the antenna with thermal deformation as the systemic error shown in Fig. 5b, the corresponding phase adjustment is shown in Fig. 7c with the largest quantity as 81.60°. The largest adjustment area is approximate corresponding to the most obvious deformation area. The comparison of the electromagnetic performance with the proposed method and the phase-only compensation is shown in Fig. 8a and the corresponding parameters are listed in Table 2. As shown in Fig. 8a and Table 2, the performance of the antenna under thermal deformation is effectively improved by both the two methods. The compensation effects are discussed as below. i.
For the sidelobe level, the increase amount of the first sidelobe is reduced by 77.11% relative to the variation amount of the IET Microw. Antennas Propag., 2018, Vol. 12 Iss. 6, pp. 954-962 © The Institution of Engineering and Technology 2017
Fig. 7 Amplitude and phase adjustments of excitation current (a) Amplitude adjustment with the proposed method (unit: dB), (b)Phase adjustment with the proposed method (unit: degree), (c) Phase adjustment with phase-only compensation (unit: degree)
Fig. 8 Comparison with the proposed and phase-only method (a) For systematic error, (b) For systematic and random error
deformed antenna with the proposed method, which is >8.47% compared to the phase-only compensation. ii. The losses of the gain are decreased to be 0.19 and 0 dB with the proposed method and the phase-only compensation, respectively, fulfilling the engineering requirement of 11.79% compared to the phase-only compensation. ii. The compensation effect of the phase-only adjustment is reducing with the expanding of the observation area. The proposed method however is effective also in the far field of sidelobe area. iii. The loss of the gain and the pointing accuracy have been compensated to satisfy the engineering requirement with both the two methods.
In conclusion, compared with the phase-only compensation method, the proposed method is able to improve the gain and pointing accuracy and more effective in the compensation for sidelobe area, not only for the first sidelobe level but also for the far sidelobe area for array antennas.
5 Experiment verification An X-band active phased array antenna with 24 × 32 elements is built and tested for the electromagnetic performance compensation, as shown in Fig. 9, including the back frame, the actuators, the array panel, and the elements array. The type of horn antenna elements are arranged in square grid with the spacing of 0.65λ. The structure size and the main material properties of the array antenna experimental model are listed in Table 3. The initial excitations of the elements are Taylor's weighted distribution in amplitude and equal phase distribution. The deformation of the antenna in the service environment is achieved by adjusting the actuators, as shown in Fig. 9, where nine actuators are installed between the back frame and the array panel with the maximum stroke of 16 mm. Digital photogrammetry is applied to obtain the deformation of the antenna. The array antenna embedded with the targets distributed on each centre position of the horn element and on the side area of the array panel is shown in Table 3 Structure size and main material parameters Components Horn element
Fig. 10 Array antenna experimental model with targets
Fig. 10. The stable reference targets on the ground are to offer a standard ratio for result data. The type of industrial measuring camera CIM-1 is applied to measure the deformation of the array antenna with the accuracy up to 3 μm. In the service process, the complexity of environmental loads could cause the antenna producing different types of structural deformation. After some deformation tests, it is found that the irregular deformation is particularly serious degrading the electrical performance of antenna. Therefore, the actuators are adjusted to simulate the type of the irregular deformation as shown in Fig. 11a. The adjustment amounts for the actuators from no. 1 to no. 9 are 1.6, 1.6, 1.6, 0.6, 0, 0.6, 4.3, 4.4, and 4.4 mm, respectively. Based on the measured deformation, the adjustment quantities of the excitation amplitude and phase are obtained from the calculation model presented in the paper, as shown in Figs. 11b and c. The attenuator and phase shifter are adjusted according to Figs. 11b and c. The performances of the antenna are measured without deformation, with deformation, and with the proposed method for compensation, respectively. In addition, the compensation effect of adjusting the phase only is also tested, with the results shown in Fig. 12. As shown in Fig. 12, the test results of the performances of array antenna are discussed as below. i.
In the main lobe area, the pointing error of 0.5° in ϕ = 90∘ plane has been fully compensated by the two methods. The gain changes in small scale and have been compensated, too.
Array panel
Actuator
Back frame
0.021 × 0.021 × 0.052
1.0 × 0.6 × 0.01
1.0 × 0.6 × 0.3
aluminium alloy
aluminium alloy
0.2 (Length) steel
aluminium alloy
Poisson's ratio
7 × 1010 0.3
7 × 1010 0.3
2.1 × 1011 0.31
7 × 1010 0.3
density, kg/m3
2.7 × 103
2.7 × 103
7.85 × 103
2.7 × 103
structure size, m material elastic modulus, Pa
960
IET Microw. Antennas Propag., 2018, Vol. 12 Iss. 6, pp. 954-962 © The Institution of Engineering and Technology 2017
Fig. 11 Measured deformation of experimental model and corresponding amplitude and phase adjustments (a) Measured deformation (unit: mm), (b) Amplitude adjustment (unit: dB), (c) Phase adjustment (unit: degree)
Fig. 12 Test performance comparison with the proposed method and phase-only compensation method (a) In ϕ = 0∘ plane, (b) In ϕ = 90∘ plane
ii. In the sidelobe area, the first sidelobe level of the antenna increases more serious in ϕ = 0∘ plane, the increase amount of the first sidelobe is reduced by 78.41% relative to the variation amount of the deformed antenna with the proposed method, which is >9.83% compared to the phase-only compensation. Moreover, the proposed method is more effective on the other field of sidelobe area in both the two planes. IET Microw. Antennas Propag., 2018, Vol. 12 Iss. 6, pp. 954-962 © The Institution of Engineering and Technology 2017
As a result, compared with the phase-only compensation, the proposed method on the one hand is capable of improving the performance of antenna in the main lobe area. On the other hand, it is also more effective in the sidelobe area. Therefore, the proposed compensation method with amplitude and phase adjusting simultaneously has the ability of compensating the performance of deformed array antenna in almost the whole area of observation. 961
6 Conclusion Complex service environment could cause the array antenna to produce structure distortion and introduce serious degradation to the electromagnetic property. However, there is little work on analysing the relationship between the adjustment amount of excitation amplitude and phase and the multi-direction deformation for planar active phased array antenna. Aiming at the difficulty of figuring out the compensation quantities of both amplitude and phase for distorted planar array antenna, a compensation method based on the structural–electromagnetic coupling model, combined with the two-dimensional fast Fourier transform is proposed in this paper. The adjustment amount of the amplitude and phase can be quickly given for planar antennas to reduce the impact of service environment. The simulation of the compensation for a thermal deformed space-based array antenna and the experiment verification of an X-band active phased array antenna with 32 × 24 elements are carried out to discuss the compensation effects with the proposed method and the phase-only adjustment method. The results shown that the proposed method with amplitude and phase adjusting simultaneously has the ability of compensating the performance of deformed array antenna in almost the whole area of observation. It is able to compensate the gain and pointing accuracy and more effective in improving the performance of antenna in sidelobe area. Meanwhile, the proposed compensation model of the excitation current can calculate the amplitude and phase adjustments when the element position errors are obtained, which provides an effective compensation method for distorted planar array antennas.
7 Acknowledgments This work was supported by the National Natural Science Foundation of China under grant no. 51522507, 51475349, and 51490660, the National 973 Program under grant no. 2015CB857100, the Youth Science and Technology Star Project of Shaanxi Province under grant no. 2016KJXX-06.
8 References [1] [2] [3] [4]
962
Haupt, R.L., Rahmat-Samii, Y.: ‘Antenna array developments: a perspective on the past, present and future’, IEEE Antennas Propag. Mag., 2015, 64, (2), pp. 86–96 Talisa, S.H., O'Haver, K.W., Comberiate, T.M., et al.: ‘Benefits of digital phased array radars’, Proc. IEEE, 2016, 104, (3), pp. 530–543 Mancuso, Y., Renard, C.: ‘New developments and trends for active antennas and TR modules’. 2014 Int. Radar Conf., Lille, France, October 2014, pp. 1–3 Takahashi, T., Nakamoto, N., Ohtsuka, M., et al.: ‘On-board calibration methods for mechanical distortions of satellite phased array antennas’, IEEE Trans. Antennas Propag., 2012, 60, (3), pp. 1362–1372
[5] [6] [7]
[8]
[9]
[10] [11] [12] [13] [14]
[15]
[16] [17]
[18] [19] [20] [21]
Parhizgar, N., Alighanbari, A., Masnadi-Shirazi, M.A., et al.: ‘Mutual coupling compensation for a practical VHF/UHF Yagi-Uda antenna array’, IET Microw. Antennas Propag., 2013, 7, (13), pp. 1072–1083 Wang, C.S., Duan, B.Y., Zhang, F.S., et al.: ‘Analysis of performance of active phased array antennas with distorted plane error’, Int. J. Electron., 2009, 96, (5), pp. 549–559 Murk, A., Schr, A., Winser, M., et al.: ‘Temperature/absorption cross integrals and the validation of radiometric temperatures for space-based radiometers’. 2016 10th European Conf. on Antennas and Propagation, IEEE, Davos, Switzerland, April 2016, pp. 1–3 Son, S.H., Yun, J.S., Park, U.H., et al.: ‘Theoretical analysis for beam pointing accuracy of stair-planar phased array antenna with tracking beam’. IEEE Antennas and Propagation Society Int. Symp., Columbus, USA, June 2003, vol. 4, pp. 204–207 Knott, P.: ‘Deformation and vibration of conformal antenna arrays and compensation techniques’. FGAN-FHR Research Institute for High Frequency Physics and Radar Techniques, Wachtberg, Germany, October 2006 Son, S.H., Eom, S.Y., Jeon, S.I., et al.: ‘Automatic phase correction of phased array antennas by a genetic algorithm’, IEEE Trans. Antennas Propag., 2008, 56, (8), pp. 2751–2754 Takano, T., Hosono, H., Saegusa, K., et al.: ‘Proposal of a multiple folding phased array antenna and phase compensation for panel steps’. IEEE AP-S & URSI, Spokane, Washington, USA, July 2011, pp. 1557–1559 Lesueur, G., Caer, D., Merlet, Th., et al.: ‘Active compensation techniques for deformable phased array antenna’. 3rd European Conf. on Antennas and Propagation, Berlin, Germany, March 2009, pp. 1578–1581 Arnold, E.J., Yan, J.B., Hale, R.D., et al.: ‘Identifying and compensating for phase center errors in wing-mounted phased arrays for ice sheet sounding’, IEEE Trans. Antennas Propag., 2014, 62, (6), pp. 3416–3421 Bürki, B., Guillaume, S., Sorber, P., et al.: ‘DAEDALUS: a versatile usable digital clip-on measuring system for total stations’. 2010 Int. Conf. on Indoor Positioning and Indoor Navigation. IEEE, Zurich, Switzerland, September 2010, pp. 1–10 Huang, G., Ma, K., Ma, T.: ‘Deformation tests of satellite antenna in the highlow temperature environment’. 2016 8th Int. Conf. on Intelligent HumanMachine Systems and Cybernetics. IEEE, Zhejiang, China, August 2016, vol. 1, pp. 78–80 Lesueur, G., Gilles, H., Girard, S., et al.: ‘Optical sensor for real time reconstruction of distortions on electronically steered antenna’, Photon. Technol. Lett., 2008, 20, (21), pp. 1763–1765 Peterman, D., James, K., Glavac, V.: ‘Distortion measurement and compensation in a synthetic aperture radar phased-array antenna’. 2010 14th Int. Symp. on Antenna Technology and Applied Electromagnetics & the American Electromagnetics Conf. IEEE, Australia, July 2010, pp. 1–5 Haugse, E.D., Ridgway, R.I., Hightower, C.H., et al.: ‘Structural deformation compensation system for large phased-array antennas’. US Patent 6333712, December 2001 Li, F.: ‘A method for detection of deformations in large phased array antennas for spaceborne synthetic aperture radars’, IEEE Trans. Antennas Propag., 1984, 32, (5), pp. 512–517 McWatters, D., Freedman, A., Michel, T., et al.: ‘Antenna auto-calibration and metrology approach for the AFRL/JPL space based radar’. Proc. of Radar Conf., Philadelphia, PA, USA, April 2004, pp. 21–26 Wang, C.S., Kang, M.K., Wang, W., et al.: ‘Electomechanical coupling based performance evaluation of distorted phased array antennas with random position errors’, Int. J. Appl. Electromagn. Mech., 2016, 51, (3), pp. 285–295
IET Microw. Antennas Propag., 2018, Vol. 12 Iss. 6, pp. 954-962 © The Institution of Engineering and Technology 2017
